Rat Locomotion Analysis Based on Straight Line Detection in Hough Space

Rat Locomotion Analysis Based on Straight Line Detection in Hough Space

This paper demonstrates a method to perform movement analysis on rats named Movement Measurement in Hough Transform Space (MMHTS). The MMHTS method consists of representing locomotion of movement based on a system of linear equations and subsequently detecting the straight lines in the Hough transfo...

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Main Authors: José Trinidad Guillen Bonilla, Héctor Guillen Bonilla, Nancy Elizabeth Franco Rodríguez, Mario Alberto García Ramírez, Alex Guillen Bonilla, Maricela Jiménez Rodríguez, María Eugenia Sánchez Morales
Format: Article
Language:English
Published: MDPI AG 2025-07-01
Series:Mathematics
Subjects:
motion analysis
image processing
movement measurement on hough transform space (MMHTS) method
hough transform
straight line detection
high application potential in motion analysis
Online Access:https://www.mdpi.com/2227-7390/13/13/2187
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Summary:This paper demonstrates a method to perform movement analysis on rats named Movement Measurement in Hough Transform Space (MMHTS). The MMHTS method consists of representing locomotion of movement based on a system of linear equations and subsequently detecting the straight lines in the Hough transform space. Four straight lines <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>L</mi></mrow><mrow><mn>0</mn></mrow></msub></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>L</mi></mrow><mrow><mn>3</mn></mrow></msub></mrow></semantics></math></inline-formula> are detected, and with their information the angles between the beelines <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>α</mi></mrow><mrow><mn>0</mn></mrow></msub></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>α</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>α</mi></mrow><mrow><mn>3</mn></mrow></msub></mrow></semantics></math></inline-formula>, intersection points <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>p</mi></mrow><mrow><mn>1</mn></mrow></msub><mfenced separators="|"><mrow><msub><mrow><mi>x</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>y</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow></mfenced></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>p</mi></mrow><mrow><mn>2</mn></mrow></msub><mfenced separators="|"><mrow><msub><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>,</mo><msub><mrow><mi>y</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></mfenced></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>p</mi></mrow><mrow><mn>3</mn></mrow></msub><mfenced separators="|"><mrow><msub><mrow><mi>x</mi></mrow><mrow><mn>3</mn></mrow></msub><mo>,</mo><msub><mrow><mi>y</mi></mrow><mrow><mn>3</mn></mrow></msub></mrow></mfenced></mrow></semantics></math></inline-formula> and their lengths <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>d</mi></mrow><mrow><msub><mrow><mi>L</mi></mrow><mrow><mn>0</mn></mrow></msub></mrow></msub></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>d</mi></mrow><mrow><msub><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow></msub></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>d</mi></mrow><mrow><msub><mrow><mi>L</mi></mrow><mrow><mn>3</mn></mrow></msub></mrow></msub></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mrow><mi>d</mi></mrow><mrow><msub><mrow><mi>L</mi></mrow><mrow><mn>4</mn></mrow></msub></mrow></msub></mrow></semantics></math></inline-formula> are measured, corresponding to the locomotion geometry of the rats’ limps. Experimentally, the MMHTS method was employed for locomotion movement and the obtained results were compared with professional design software, detecting the following miscalculations: 0.144° for the angle measurements, 0.131 for the length measurement and 0.139 for the point detection. Based in the measurements results and the calculated errors, the MMHTS method is efficient and exhibits a high application potential in motion analysis.
ISSN:2227-7390

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